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:<math>E_{xc}^{\mathrm{LDA}}[\rho] = \int \rho(\mathbf{r})\epsilon_{xc}(\rho)\ \mathrm{d}\mathbf{r}\ ,</math>
where ''ρ'' is the [[electronic density]] and ''ε''<sub>xc</sub>, the exchange-correlation energy density, is a function of the density alone. The exchange-correlation energy is decomposed
:<math>E_{xc} = E_x + E_c\ ,</math>
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